No. Every smooth bundle over $S^1$ with fiber $M$ is the mapping torus of some diffeomorphism $f:M\to M$. Isomorphism classes of bundles correspond to conjugacy classes in the group of isotopy classes of diffeomorphisms.

There are already surprises when $M$ is $S^n$. For example, an exotic $7$-sphere can be realized as the union of two copies of $D^7$ glued by a diffeomorphism of $S^6$ that is not isotopic to the identity, and this leads to examples.

There are related examples with $M=P^n$.

There are certainly

No. Every smooth bundle over $S^1$ with fiber $M$ is the mapping torus of some diffeomorphism $f:M\to M$. Isomorphism classes of bundles correspond to conjugacy classes in the group of isotopy classes of diffeomorphisms.

There are already surprises when $M$ is $S^n$. For example, an exotic $7$-sphere can be realized as the union of two copies of $D^7$ glued by a diffeomorphism of $S^6$ that is not isotopic to the identity, and this leads to examples.

There are related examples with $M=P^n$.